The group presented amendments to the bill on Thursday, including one asking that a law that would make it possible for one partner in a same-sex couple to adopt the other partner's biological child be scrapped.
They have instead asked that the measure be replaced with a form of foster care.
The website, Gay.it, sparked controversy after publishing the names of the 30 Catholic senators from the centre-left party who have cast doubt over the 'stepchild adoption' measure of the controversial bill, on which the Senate is due to vote on January 28th.
Renzi has been fervently pushing to get the legislation, a cornerstone of his mandate, passed, especially as Italy is the last major state in western Europe not to offer gay couples any legal rights.
Opposition to the ‘stepchild adoption' measure has been widely voiced by Renzi's main coalition partner, the New Centre Right party led by Angelino Alfano, and the Union of the Centre party.
Silvio Berlusconi has also come out and said that his Forza Italia party would vote against the measure, despite supporting a civil unions bill.
But this is the first inkling that members of the Democratic Party may vote against.
Tension over the measure has been brewing within the party in recent days, with Renzi saying members should vote according to their conscience rather than toe the party line.
The group, which included Giorgio Tonini, Roberto Cociancich, Nicola Latorre and Nicoletta Favero, have asked that the list on Gay.it be removed, Il Fatto Quotidiano reported.
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“Not only is this a despotic action,” Tonino argued.
“But it's an irresponsible act which recalls distant ghosts that would be best left in the past. Exposing a group of senators for expressing an opinion against stepchild adoption will not split the Democratic party, but is likely to slow the passing of the measure on civil unions.”
Nicoletta Favero said: “Who said expressing an opinion on part of the bill was the same as not wanting to vote on it?”